Answer:
The answer is below
Step-by-step explanation:
A function shows the relationship that exist between two variables (the independent variable and dependent variable). The independent variable does not depend on any variable and is known as the input while the dependent variable depends on other variable and is known as the output.
The relationship between two variables of a linear function i.e y (dependent variable) and x (independent variable) represented by the points [tex](x_1,y_1)\ and\ (x_2,y_2)[/tex] is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
a) Write an expression for q as a linear function of p.
To do this, q is the dependent variable and p is the independent variable. From the table. the variables can be represented by (1, 18) and (2, 12)
Hence:
[tex]q-18=\frac{12-18}{2-1}(p-1)\\ \\q-18=-6(p-1)\\\\q-18=-6p+6\\\\q=-6p+24[/tex]
b) Write an expression for p as a linear function of q.
To do this, p is the dependent variable and q is the independent variable. From the table. the variables can be represented by (18, 1) and (12, 2)
Hence:
[tex]p-1=\frac{2-1}{12-18}(q-18)\\ \\p-1=-\frac{1}{6}(q-18)\\\\p-1=-\frac{1}{6}q+3\\\\p=-\frac{1}{6}q+4[/tex]
